Statistical Models in R - University of Notre Dame
Statistical Models
Statistical Models in R
Some Examples Steven Buechler
Department of Mathematics 276B Hurley Hall; 1-6233
Fall, 2007
Statistical Models
Outline
Statistical Models Linear Models in R
Statistical Models
Regression
Regression analysis is the appropriate statistical method when the response variable and all explanatory variables are continuous. Here, we only discuss linear regression, the simplest and most common form.
Remember that a statistical model attempts to approximate the response variable Y as a mathematical function of the explanatory variables X1, . . . , Xn. This mathematical function may involve parameters. Regression analysis attempts to use sample data find the parameters that produce the best model
Statistical Models
Linear Models
The simplest such model is a linear model with a unique explanatory variable, which takes the following form.
y^ = a + bx.
Here, y is the response variable vector, x the explanatory variable, y^ is the vector of fitted values and a (intercept) and b (slope) are real numbers. Plotting y versus x, this model represents a line through the points. For a given index i, y^i = a + bxi approximates yi . Regression amounts to finding a and b that gives the best fit.
Statistical Models
Linear Model with 1 Explanatory Variable
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